Quantitative and qualitative cohomological properties for non-Kähler manifolds

Angella, Daniele; Tardini, Nicoletta

doi:10.1090/proc/13209

Quantitative and qualitative cohomological properties for non-Kähler manifolds
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by Daniele Angella and Nicoletta Tardini

Proc. Amer. Math. Soc. 145 (2017), 273-285

DOI: https://doi.org/10.1090/proc/13209

Published electronically: July 12, 2016

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Abstract:

We introduce a “qualitative property” for Bott-Chern cohomology of complex non-Kähler manifolds, which is motivated in view of the study of the algebraic structure of Bott-Chern cohomology. We prove that such a property characterizes the validity of the $\partial \overline \partial$-Lemma. This follows from a quantitative study of Bott-Chern cohomology. In this context, we also prove a new bound on the dimension of the Bott-Chern cohomology in terms of the Hodge numbers. We also give a generalization of this upper bound, with applications to symplectic cohomologies.

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